Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 4 }$ without using a calculator.
A) $- 1$
B) $- 2$
C) $- 3$
D) $4$
E) $\frac { 1 } { 4 }$

Question

Quizplus · Accepted Answer

The function $f(x) = \log_2 x$ asks for the power to which 2 must be raised to get $x$. For $x = \frac{1}{4}$, we know that $2^{-2} = \frac{1}{2^2} = \frac{1}{4}$. Therefore, $f\left(\frac{1}{4}\right) = \log_2 \left(\frac{1}{4}\right) = -2$.

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Evaluate the Function $f ( x ) = \log _ { 2 } x$